The first and the secund-order rogue wave solutions illustrated in this paper resemble those obtained in Ref [1]}. In this reference paper, the authors used a non-recursive DT. At our knowledge, the third-order rogue wave solutions for the Manakov system and a generalized formula for generating more than third-order have not yet been constructed. Thus, we actually believe that the present work is worth underlying and paves ways for further investigations of the system above within the viewpoint of the existence of propagation of extreme wave excitations. The observation of these rogue waves profiles is expected to be possible in Manakov or near-Manakov systems such as birefringent fiber transmission links ([2]},[3]}-[4]} ), crossing sea waves [5]}, photorefractive media [6]}, AlGaAs planar waveguide [7]} and so on.
